[plt-scheme] Natural numbers

On Wed, Mar 11, 2009 at 10:25:33PM -0400, Stephen Bloch wrote:
> 
> On Mar 11, 2009, at 8:33 PM, Norman Gray wrote:
> 
> >In maths, the term "the natural numbers" refers specifically to the  
> >set of positive integers (see for example [1]), and not to any set  
> >isomorphic to that.  Thus it does not depend on what you or I may  
> >or may not find natural, and its meaning is not really a matter for  
> >dispute.  Anyone who refers, in any sort of semi-formal context, to  
> >"the natural numbers" as meaning anything other than {n in Z : n >  
> >0} is being quixotic.
> 
> I was brought up with "the natural numbers" meaning {n in Z : n >=  
> 0}.  In both my dissertation and my advisor's, and many of the  
> published papers in my field, it is quite important that the natural  
> numbers include zero.  In fact, I think it's been years if not  
> decades since I saw "the natural numbers" used formally in a sense  
> that excluded zero.
> 
> >I don't believe computer scientists have a get-out-of-jail-free  
> >card here.
> 
> Ah, maybe that's it: I went through graduate school surrounded by  
> logicians and computer scientists. :-)
> 
> 
> Then again, if you ask my programming students, you'll get about a  
> 50/50 split on the question of whether zero is positive....

That would make sense if half of them grew up on old one's complement 
machines, which has a separate plus zero and minus zero in their binary 
representations.  But that would probably have to be the over-fifty 
crowd.  Do you teach senior citicens?

-- hendrik